Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
1
Laws of nature
The notion of a law of nature is fundamental to science. In one sense this is obvious, in
that much of science is concerned with the discovery of laws (which are often named
after their discoverers hence Boyle’s law, Newton’s laws, Ostwald’s law, Mendel’s laws,
and so on). If this were the only way in which laws are important, then their claim to
be fundamental would be weak. After all, science concerns itself with much more than
just the uncovering of laws. Explaining, categorizing, detecting causes, measuring, and
predicting are other aims of scientific activity, each quite distinct from law-detecting. A
claim of this book is that laws are important because each of these activities depends on
the existence of laws. For example, take Henry Cavendish’s attempt to measure the
gravitational constant G using the torsion balance. If you were to have asked him what
this constant is, he would have told you that it is the ratio of the gravitational force
between two objects and the product of their masses divided by the square of their
separation. If you were then to ask why this ratio is constant, then the answer would
be that it is a law of nature that it is so. If there were no law of gravitation, then
there would be no gravitational constant; and if there were no gravitational constant
there would be nothing that counts as the measurement of that constant. So the
existence and nature of a law was essential to Cavendish’s measuring activities.
Somewhat contentiously, I think that the notion of explanation similarly depends upon
that of law, and even more contentiously I think that causes are also dependent on
laws. A defence of these views must wait until the next chapter. I hope it is clear
already that laws are important, a fact which can be seen by considering that if there
were no laws at all the world would be an intrinsically chaotic and random place in
which science would be impossible. (That is assuming that a world without laws could
exist - which I am inclined to think doubtful, since to be any sort of thing is to be
subject to some laws.) Therefore, in this chapter we will consider the question: What
is a law of nature? Upon our answer, much that follows will depend.
Before going on to discuss what laws of nature are, we need to be clear about what
laws are not. Laws need to be distinguished from statements of laws and from our
theories about what laws there are. Laws are things in the world which we try to
discover. In this sense they are facts or are like them. A statement of a law is a linguistic item and so need not exist, even though the corresponding law exists (for
instance if there were no people to utter or write statements). Similarly, theories are
human creations but laws of nature are not. The laws are there whatever we do -- one
of the tasks of the scientist is to speculate about them and investigate them. A
scientist may come up with a theory that will be false or true depending on what the
laws actually are. And, of course, there may be laws about which we know nothing. So,
for instance, the law of universal gravitation was discovered by Newton. A statement
of the law, contained in his theory of planetary motion, first appeared in his Principia
mathematica. In the following we are interested in what laws are -- that is, what sort
of thing it was that Newton discovered, and not in his statement of the law or his
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
2
theories containing that statement.8 Furthermore, we are not here asking the question:
Can we know the existence of any laws? Although the question “What is an X?” is
connected to the question “How do we know about Xs?”, they are still distinct
questions. It seems sensible to start with the former -- after all, if we have no idea
what Xs are, we are unlikely to have a good answer to the question of how we know
about them.
1. Minimalism about laws - the simple regularity theory
In the Introduction we saw that the function of (Humean) induction is to take us from
observations of particular cases to generalizations. It is reasonable to think that this is
how we come to know laws -- if we can come to know them at all. Corresponding to a
true inductive conclusion, a true generalization, will be a regularity. A regularity is just
a general fact. So one inductive conclusion we might draw is that all emeralds are green,
and another is that all colitis patients suffer from anaemia. If these generalizations are
true, then it is a fact that each and every emerald is green and that each and every
colitis sufferer is anaemic. These facts are what I have called regularities. The first
view of laws I shall consider is perhaps the most natural one. It is that laws are just
regularities.
This view expresses something that I shall call minimalism about laws. Minimalism
takes a particular view of the relation between a law and its instances. If it is a law
that bodies in free fall near the surface of the Earth accelerate towards its centre at 9.8
ms−2, then a particular apple falling to the ground and accelerating at 9.8 ms−2 is an
instance of this law. The minimalist says that the law is essentially no more than the
collection of all such instances. There have been, and will be, many particular instances,
some observed but most not, of objects accelerating towards the centre of the Earth at
this rate. The law, according to the minimalist, is simply the regular occurrence of its
instances. Correspondingly, the statement of a law will be the generalization or
summary of these instances.
Minimalism is an expression of empiricism, which, in broad terms, demands that
our concepts be explicable in terms that relate to our experiences. Empiricist
minimalism traces its ancestry at least as far back as David Hume. By defining laws in
terms of regularities we are satisfying this requirement (as long as the facts making up
the regularities are of the sort that can be experienced). Later we shall come across an
approach to laws that is not empiricist.
The simplest version of minimalism says that laws and regularities are the same.
This is called the simple regularity theory (SRT) of laws.
SRT: It is a law that Fs are Gs if and only if all Fs are Gs.
8 It must be admitted that scientists’ (and philosophers’) usage is a bit loose in this regard. We do talk about
Kepler’s laws and the ideal gas laws, and in doing so we must be talking about certain statements or theories - for there are no such laws, these theories being only close approximations to the truth.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
3
While the SRT has the merit of simplicity it suffers from the rather greater demerit
that it is false. If it were true, then all and only regularities would be laws. But this is
not the case.
The most obvious problem is that the existence of a simple regularity is not
sufficient for there to be a corresponding law, i.e. there are simple regularities that are
not laws. A criticism is also made that it is not even necessary for there to be a
regularity for the corresponding law to exist. That is, there are laws without the
appropriate regularities.
Regularities that are not laws
I will start with the objection that being a regularity is not sufficient for being a law.
Consider the following regularities:
(a) All persisting lumps of pure gold-195 have a mass less than 1,000 kg.
(b) All persisting lumps of pure uranium-235 have a mass of less than 1,000 kg.9
Both (a) and (b) state true generalizations. But (a) is accidental and (b) is law-like.
It is no law that there are no lumps of the pure isotope of gold -- we could make one if
we thought it worth our while. However, it is a law that there are no such lumps of
uranium-235, because 1,000 kg exceeds the critical mass of that isotope (something less
than a kilogram) and so any such lump would cause its own chain reaction and
self-destruct. What this shows is that there can be two very similar looking
regularities, one of which is a law and the other not.
This is not an isolated example. There are an indefinite number of regularities that
are not laws. Take the generalization: all planets with intelligent life forms have a
single moon. For the sake of argument, let us imagine that the Earth is the only planet
in the universe with intelligent life and that there could exist intelligent life on a planet
with no moons or more than one. (For all I know, these propositions are quite likely to
be true.) Under these circumstances, the above generalization would be true, even
though there is only one instance of it. But it would not be a law; it is just a coincidence. The point here is that the SRT does not distinguish between genuine laws and
mere coincidences. What we have done is to find a property to take the place of F
which has just one instance and then we take any other property of that instance for
G. Then “All Fs are Gs’’ will be true. And, with a little thought, we can find any
number of such spurious coincidental regularities. For most things that there are we
could list enough of their general properties to distinguish one thing from everything
else. So, for instance, with a person, call her Alice, we just list her hair colour, eye
colour, height, weight, age, sex, other distinguishing features, and so on in enough detail
that only Alice has precisely those qualities. These qualities we bundle together as a
single property F. So only Alice is F. Then choose some other property of Alice (not
necessarily unique to her), say the fact that she plays the oboe. Then we will have a
9 Examples of this sort are to be found in the writings of Carl Hempel and Hans Reichenbach.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
4
true generalization that all people who are F (i.e. have fair hair, green eyes, are 1.63 m
tall, weigh 59.8 kg, have a retrousse nose, etc.) play the oboe. But we do not want to
regard this as a law, since the detail listed under F may have nothing whatsoever to do
with an interest in and talent for playing the oboe.
The minimalist who wants to defend the SRT might say that these examples look
rather contrived. First, is it right to bundle a lot of properties together as one
property F? Secondly, can just one instance be regarded even as a regularity? (If it is
not a regularity then it will not be a counterinstance.) However, I do not think that
the minimalist can make much headway with these defences.
To the general remark that the examples look rather contrived, the critic of the SRT
has two responses. First, not all the cases are contrived, as we can see from the gold
and uranium example. We can find others. One famous case is that of Bode’s “law” of
planetary orbits. In 1772, J. E. Bode showed that the radii of known planetary orbits
fit the following formula: 0.4 + 0.3 × 2n (measured in astronomical units) where n = 0
for Venus, 1 for the Earth, 2 for Mars, and so on, including the minor planets.
(Mercury could be included by ignoring the second term, its orbital radius being 0.4
astronomical units.) Remarkably, Bode’s law was confirmed by the later discovery of
Uranus in 1781. Some commentators argued that the hypothesis was so well confirmed
that it achieved the status of a law, and consequently ruled out speculation concerning
the existence of a possible asteroid between the Earth and Mars. Bode’s “law” was
eventually refuted by the observation of such an asteroid, and later by the discovery of
the planet Neptune, which did not fit the pattern. What Bode’s non-law shows is that
there can be remarkable uniformities in nature that are purely coincidental. In this case
the accidental nature was shown by the existence of planets not conforming to the
proposed law. But Neptune, and indeed Pluto too, might well have had orbits fitting
Bode’s formula. Such a coincidence would still have been just that, a coincidence, and
not sufficient to raise its status to that of a law.
Secondly, the critic may respond that the fact that we can contrive regularities is
just the point. The SRT is so simple that it allows in all sorts of made-up regularities
that are patently not laws. At the very least the SRT will have to be amended and
sharpened up to exclude them. For instance, taking the first specific point, as I have
stated it the SRT does not specify what may or may not be substituted for F and G.
Certainly it is an important question whether compounds of properties are themselves
also properties. In the Alice example I stuck a whole lot of properties together and
called them F. But perhaps sticking properties together in this way does always yield a
new property. In which case we might want to say that only uncompounded properties
may be substituted for F and G in the schema for the SRT.
However, amending the SRT to exclude Fs that are compound will not help matters
anyway, for two reasons. First, there is no reason why there should not be
uncompounded properties with unique instances. Secondly, some laws do involve
compounds -- the gas laws relate the pressure of a gas to the compound of its volume
and temperature. To exclude regularities with compounds of properties would be to
exclude a regularity for which there is a corresponding law. To the second point, that
the regularities constructed have only one instance, one rejoinder must be this: why
cannot a law have just one instance? It is conceivable that there are laws the only
instance of which is the Big Bang. Indeed, a law might have no instances at all. Most
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
5
of the transuraniurn elements do not exist in nature and must be produced artificially
in laboratories or nuclear explosions. Given the difficulty and expense of producing
these isotopes and because of their short half-lives it is not surprising that many tests
and experiments that might have been carried out have not been. Their electrical
conductivity has not been examined, nor has their chemical behaviour. There must be
laws governing the chemical and physical behaviour of these elements under circumstances which have never and never will arise for them. There must be facts about
whether nobelium-254, which is produced only in the laboratory, burns in oxygen and,
if so, what the colour of its flame is, what its oxide is like, and so forth; these facts will
be determined by laws of nature, laws which in this case have no instances.
So we do not want to exclude something from being a law just because it has few
instances, even just one instance, or none at all. At the same time the possibility of
instanceless laws raises another problem for the SRT similar to the first. According to
the SRT empty laws will be empty regularities - cases of “all Fs are Gs” where there are
no Fs. There is no problem with this; it is standard practice in logic to regard all
empty generalizations as trivially true.10 What is a problem is how to distinguish those
empty regularities that are laws from all the other empty regularities. After all, a
trivial empty regularity exhibits precisely as much regularity as an empty law.
Let us look at a different problem for the SRT. This concerns functional laws. The
gas law is an example of a functional law. I t says that one magnitude -- the pressure of
a body of gas -- is a function of other magnitudes, often expressed in a formula such as:
P = kT/V
where P is pressure, T is temperature, V is volume, and k is a constant. In regarding
this as a law, we believe that T and V can take any of a continuous range of values,
and that P will correspondingly take the value given by the formula. Actual gases will
never take all of the infinite range of values allowed for by this formula. In this respect
the formula goes beyond the regularity of what actually occurs in the history of the
universe. But the SRT is committed to saying that a law is just a summary of its
instances and does not seek to go beyond them. If the simple regularity theorist sticks
to this commitment, the function ought to be a partial or gappy one, leaving out values
that are not actually instantiated. Would such a gappy “law” really be a law? One’s
intuition is that a law should cover the uninstantiated values too. If the SRT is to be
modified to allow filling in of the gaps, then this needs to be justified. Furthermore, the
filling in of the gaps in one way rather than another needs justification. Of course
there may well be a perfectly natural and obvious way of doing this, such as fitting a
simple curve to the given points. The critic of the SRT will argue that this is justified
because this total (non-gappy) function is the best explanation of the instantiated
values. But the simple regularity theorist cannot argue in this way, because this
argument accepts that a law is something else other than the totality of its instances.
As far as what actually occurs is concerned, one function which fits the points is as
10 According to this view, the claim that all living dodos live in Australia is true; and it is also true that all
living dodos live in Switzerland. Perhaps it is odd to regard such statements as true, but if we do not regard
them as such we cannot count any of the empty generalizations about the artificial elements as being true -but some must be, namely those that correspond to laws.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
6
good as any other. From the SRT point of view, the facts cannot decide between two
such possible functions. But, if the facts do not decide, we cannot make an arbitrary
choice, say choosing the simplest for the sake of convenience, as this would introduce an
arbitrary element into the notion of lawhood. Nor can we allow all the functions that
fit the facts to be laws. The reason for this is the same as the reason why we cannot
choose one arbitrarily and also the same as the reason why we cannot have all empty
generalizations as laws. This reason is that we expect laws to give us determinate
answers to questions of what would have happened in counterfactual situations -- that
is situations that did not occur, but might have.
Laws and counterfactuals
Freddie’s car is black and when he left it in the sun it got hot very quickly. The
statement “Had Freddie’s car been white, it would have got hot less quickly” is an
example of a counterfactual statement. It is not about what did happen, but what
would have happened in a possible but notactual (a counter-to-fact) situation (i.e.
Freddie’s car being white rather than black). The counterfactual in question is true.
And it is true because it is a law that white things absorb heat less rapidly than black
things. Laws support counterfactuals.
We saw above that every empty regularity will be true and hence will be a law,
according to the SRT. This is an undesirable conclusion. Counterfactuals help us see
why. Take some property with no instances, F. If we allowed all empty regularities to
be laws we would have both law 1 “it is a law that Fs are Gs’’ and law 2 “it is a law
that Fs are not-Gs". What would have happened if a, which is not F had been F?
According to law 1, a would have been G, while law 2 says a would have been not-G.
So they cannot both really be laws. Similarly, we cannot have both of two distinct
functions governing the same magnitudes being laws, even if they agree in their values
for actual instances and diverge only for non-actual values. For the two functional laws
will contradict one another in the conclusion of the counterfactuals they support when
we ask what values would P have taken had T and V taken such-and-such (non-actual)
values.
Counterfactuals also underline the difference between accidental and nomic
regularities. Recall the regularities concerning very large lumps of gold and uranium
isotopes. There are no such lumps of either. In the case of uranium-235, there could
not be such lumps, there being a law that there are no such lumps. On the other
hand, there is no law concerning large lumps of gold, and so there could have been
persisting 2,000 kg lumps of gold-195. In this way counterfactuals distinguish between
laws and accidents.
Some philosophers think that the very fact that laws support counterfactuals is
enough to show the minimalist to be wrong (and the SRT supporter in particular).
The reasoning is that counterfactuals go beyond the actual instances of a law, as they
tell us what would have happened in possible but non-actual circumstances. And so
the minimalist must be mistaken in regarding laws merely as some sort of summary of
their actual instances. This argument seems powerful, but I think it is not a good line
for the anti-minimalist to pursue. The problem is that counterfactuals are not any
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
7
better understood than laws, and one can argue that our understanding of
counterfactuals is dependent on our notion of law or something like it, in which case
corresponding to the minimalist account of laws will be a minimalist account of
counterfactuals.11 You can see that this response is plausible by considering that
counterfactuals are read as if there is a hidden clause, for instance “Freddie’s car would
have got hot less quickly had it been white and everything else and been the same as far
as possible”. (Which is why one cannot reject the counterfactual by saying that had
Freddie’s car been white, the Sun might not have been shining.) The clause which says
that everything should be the same as far as possible requires among other things, like
the weather being the same, that the laws of nature be the same. So one can say that
laws support counterfactuals only because counterfactuals implicitly refer to laws.
Counterfactuals therefore have nothing to tell us about the analysis of laws. Consider
the fact that laws do not support all counterfactuals -- particularly those
counterfactuals relating to the way things would be with different laws. For instance
one could ask how quickly would two things have accelerated towards one another had
the gravitational constant G been twice what it is. The actual law of gravitation clearly
does not support the correct answer to this counterfactual question.
Laws that are not regularities: probabilistic laws
So far there is mounting evidence that being a simple regularity is not sufficient for
being a law. There are many regularities that do not constitute laws of nature:
(a)
(b)
(c)
(d)
accidental regularities
contrived regularities
uninstantiated trivial regularities
competing functional regularities.
The natural response on the part of the minimalist is to try to amend the SRT by
adding further conditions that will reduce the range of regularities which qualify as
laws. So the original idea is maintained, that a law is a regularity, and with an
appropriate amendment it will now be that laws are a certain sort of regularity, not
any old regularity.
This is the line I will examine shortly. But before doing so I want to consider an
argument which suggests that being a regularity is not even sufficient for being a law.
That is, there are law’s that are not simple regularities. If this line of thinking were
correct, then it would be no good trying to improve the SRT by adding extra
conditions to cut down the regularities to the ones we want, as this would still leave
out some laws that do not have a corresponding regularity.
The problem concerns probabilistic laws. Probabilistic laws are common in nuclear
physics. Atomic nuclei as well as individual particles are prone to decay. This tendency
to decay can be quantified as the probability that a nucleus will decay within a certain
11 Such accounts are provided by J. L. Mackie and David Lewis, whose views on counterfactuals are, despite
superficial dissimilarites, closely related.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
8
period. (When the probability is one-half, the corresponding period of time is called the
half-life.) So a law of nuclear physics may say that nuclei of a certain kind have a
probability p of decaying within time t. What is the regularity here? The SRT, as it
stands, has no answer to this question. But an answer, which satisfies the minimalist’s
aim of portraying laws as summaries of the individual facts, is this. The law just
mentioned will be equivalent to the fact that, of all the relevant particles taken
together, a proportion p will have decayed within t. (Note that we would find out
what the value of p is by looking at the proportion that decays in observed samples.
Another feature that might be included in the law is resiliency, i.e. that p is the
proportion which decays in all appropriate subpopulations, and not just the population
as a whole.)
The problem arises when we consider each of the many particles individually. Each
particle has a probability p of decaying in time t. This is perfectly consistent with the
particle decaying well before t or well after t. So the law allows for any particle to decay
only after time t* which is later than t. And what goes for one particle goes for all.
Thus the law is consistent with all the particles decaying only after t*, in which case
the proportion decaying by t is zero. This means that we have a law the instances of
which do not form the sort of regularity the minimalist requires. The minimalist
requires the proportion p to decay by t. We would certainly expect that. But this is by
no means necessary. While it is extremely unlikely that no particle will decay until after
t, it is not impossible. Another, less extreme, case would be this. Instead of the
proportion p decaying within t, a very slightly smaller proportion than p might decay.
The chance of this is not only greater than zero, i.e. a possibility, but may even be quite
high.
The minimalist’s guiding intuition is that the existence and form of a law is
determined by its instances. Here we have a case where our intuitions about laws allow
for a radical divergence between the law and its instances. And so such a law is one
which could not be a regularity of the sort required by the minimalist. This would
appear to be a damning argument against minimalists, not even allowing for an
amendment of their position by the addition of extra conditions. Nonetheless, I think
the argument employed against the minimalist on this point could be seen as simply
begging the question. The argument starts by considering an individual particle
subject to a probabilistic law. The law might be that such particles have a half-life of
time t. The argument points out that this law is consistent with the particle decaying
at time t* after t. This is all true. The argument then proceeded to claim that any
collection could, therefore, be such that all its particles decay after t, including the
collection of all the particles over all time.
The form of this argument is this: what is possible for any individual particle is
possible for a collection of particles; or, more generally, if it is possible that X, and it is
possible that Y, and it is possible that Z, and so on, then it is possible that X and Y
and Z, etc. This form of argument certainly is not logically valid. Without looking
outside, I think to myself it is possible that it is raining and it is possible that it is not
raining, but I certainly should not conclude that it is possible that it is both raining
and not raining. More pertinent to this issue is another counter-example. It is possible
for one person to be taller than average, but it is not possible for everyone to be taller
than average. This is because the notion of an average is logically related to the
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
9
properties of a whole group. What this suggests is that the relevant step in the
argument against the minimalist could only be valid if there is a logical gap between a
law and the collection of its instances. But this is precisely what the minimalist denies.
For, on the contrary, the minimalist claims that there is no gap; rather there is an
intimate logical link in that the probabilistic law is some sort of sophisticated averaging
out over its instances. So it turns out that the contentious step in the argument is
invalid or, at best, question begging against the minimalist.
Still, even if the argument is invalid, it does help alert our intuitions to an
implausibility with minimalism. We may not be able to prove that there can be a gap
between the chance of decay that each atom has and the proportion of particles
actually decaying -- but the fact that such a gap does seem possible is evidence against
the minimalist.
2. The systematic account of laws of nature
We have seen so far that not all regularities are also laws, though it is possible for the
minimalist to resist the argument that not all laws are regularities. What the
minimalist needs to do is to find some further conditions, in addition to being a
regularity, which will pare down the class of regularities to just those that are laws.
Recall that the minimalist wants laws simply to generalize over their instances. Law
statements will be summaries of the facts about those instances. If this is right we
should not expect every regularity to be a law. For we can summarize a set of facts
without having to mention every regularity that they display, and an efficient summary
would only record sufficient regularities to capture all the facts in which we are
interested. Such a summary would be systematic; rather than being a list of separate
regularities, it would consist of a shorter list of interlocking regularities, which together
are enough to encapsulate all the facts. It would be as simple as possible, but also as
strong as possible, capturing as many facts and possible facts as it can.
What I mean here by “capturing” a fact is the subsuming of that fact under some
law. We want it to be that laws capture all and only their instances. So if the fact is
that some object a has the property G, then this would be captured by a law of the
form all Fs are Gs (where a is F). For example, if the fact we are interested in is the
explosive behaviour of a piece of lithium, then this fact can be captured by the law that
lithium reacts explosively on contact with water (if in this case it was in contact with
water). If the fact is that some magnitude M has the value m then the fact is captured
by a law of the form M = f(X, Y, Z .... ) (where the value of X is x, the value of Y is y,
etc., and m = f(x, y, z .... ). An example of this might be the fact that the current
through a circuit is 0.2 A. This fact can be captured by Ohm’s law V = IR, if for
instance there is a potential difference of 10 V applied to a circuit that has a resistance
of 50 W. As we shall see in the next chapter, this is tantamount to saying that the
facts in question have explanations. If a fact has an explanation according to one law,
we do not need another independent law to explain the same fact. Let it be the case
that certain objects, a, b, c, and d are all G. Suppose that they are also all F and also
the only Fs that there are. We might think then that it is a law that Fs are Gs and
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
10
that this law explains why each of the objects is G. But we could do without this law
and the explanations it furnishes if it is better established that there is a law that Hs
are Gs and a is H, and that there is a law that Js are Gs and that b is J, and that
there is a law that Ks are Gs and that c is K, and so on. In this case the proposed law
that Fs are Gs is redundant. We can instead regard the fact that all Fs are Gs as an
accidental regularity and not a law-like one. If we symbolize “a is F” by “Fa”, then as
Figure 1.1 shows, we could organize the facts into an economical system with three
rather than four laws.
Ga
Fa
Ha
Gb
Fb
Jb
Gc
Fc
Kc
Gm
Hm
Gp
Jp
Gr
Kr
Gn
Hn
Gq
Jq
Gs
Ks
]
Accidental regularity
that all Fs are Gs
Law that Ks are Gs
Law that Js are Gs
Law that Hs are Gs
Figure 1. 1
This organizing of facts into an economical system allows us to distinguish between
accidental regularities and laws. This was one of the problems facing the SRT. The
systematic approach does better. It also easily accommodates the other problem case,
functional laws. The simplest way of systematizing a collection of distinct points on a
graph is to draw the simplest line through them. And we will only want one line, as
adding a second line through the same points will make the- system much less simple
without adding to the power of the system, because the first line already captures the
facts we are interested in. Thus in a systematic version of minimalism we will have
non-gappy functional laws that are unique in their domain.
These are the virtues of the account of laws first given by Frank Ramsey and later
developed by David Lewis.12 The idea is that we regard the system as axiomatized,
that is to say we boil the system down to the most general principles from which the
regularities that are laws follow. A collection of facts may be axiomatized in many (an
infinite number of) ways. So the appropriate axiomatization will be that which, as
discussed above, is as simple as possible and as strong as possible. The strength of a
12 See Lewis, Counterfactuals, pp. 72-77. Lewis refers (p. 73) to an unpublished note by F. P. Ramsey.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
11
proposition can be regarded as its informativeness. So, considering (a) all emeralds are
green, (b) all emeralds are coloured, and (c) all South American emeralds are green, (a)
is more informative and so stronger than both (b) and (c).
Formally, the systematic account says:
A regularity is a law of nature if and only if it appears as a theorem or axiom in
that true deductive system which achieves a best combination of simplicity and
strength.
Remember that this is a “God’s eye” view, not ours, in the sense that we do not know
all the facts that there are and so do not know in that direct way what the best
axioniatization of them is. What we are saying is that this is what a law of nature is.
Our ignorance of the best axiomatization of everything ignorance of the laws of nature.
Of course we are not entirely ignorant of them. If science is any good we know some of
them, or approximations to them at any rate. And it can be said in support of Ramsey
and Lewis, that the sorts of thing we look for in a theory which proposes a law of
nature are precisely what they say something ought to have in order to be a law. First
we look to see whether it is supported by evidence in the form of instances, i.e. whether
it truly is a regularity. But we will also ask whether it is simple, powerful, and
integrates with the other laws we believe to exist.
The systematic view is not entirely without its problems. First, the notion of
simplicity is important to the systematic characterization of law, yet simplicity is a
notoriously difficult notion to pin down. In particular, one might think that simplicity
is a concept which has a significant subjective component to it. What may appear
simple to one person might look rather complex to another. In which case the concept
of law would also have a subjective element that conflicts with our intuition that laws
are objective and independent of our perspective. Another way of looking at the
problem of simplicity is to return to Goodman’s puzzle about the concept “grue”. The
fact that we can replace the simple looking “X is grue” by the complex looking “either X
is green and observed before midnight on 31 December 2000 or X is blue and not
observed before midnight on 31 December 2000”, and vice versa, shows that we cannot
be sure of depending merely on linguistic appearance to tell us the difference. The
simple law that emeralds are green appears to be the same as the complex law that
emeralds are grue, if observed before midnight on 31 December 2000, or bleen if not
observed before midnight on 31 December 2000. Without something like a solution to
Goodman’s problem we have no reason to prefer one set of concepts to another when
trying to pin down the idea of simplicity.
The second problem with the systematic view is that as I have presented it, i.e. it
presumes there is precisely one system that optimally combines strength and simplicity.
For a start it is not laid down how we are supposed to weigh simplicity and strength
against one another. We could add more laws to capture more potential facts and thus
gain strength, but with a loss in simplicity. Alternatively, we might favour a simpler
system that has less strength. Again there is the suspicion that the minimalist’s
answer to this problem may be objectionably subjective. Even if there is a clear and
objective way of balancing these two, it may yet turn out that two or more distinct
systems do equally well. So which are our laws? Perhaps something is a law if it
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
12
appears in any one of the optimal systems. But this will not do, because the different
systems might have conflicting laws that lead to incompatible counterfactuals. On the
other hand, we may be more restrictive and accept as laws only those regularities that
appear in all the optimal systems.13 However, we may find that there are very few such
common regularities, and perhaps none at all.
Basic laws and derived laws
It is a law-like and true (almost) generalization that all objects of 10 kg when subjected
to a force of 40 N accelerate at 4 m s−2. But this generalization would not feature as an
axiom of our system, because it would be more efficient to have the generalization that
the acceleration of a body is equal to the ratio of the resultant force acting upon it and
its mass. By having that generalization we can dispense with the many generalizations
that mention specific masses, forces, and accelerations. From the overarching
generalization these more specific ones may be derived. That is to say, our system will
be axiomatic; it will comprise the smallest set of laws from which it is possible to deduce
all other laws. This shows an increase in simplicity -- few generalizations instead of
many -- and in strength, as the overarching generalization will have consequences not
entailed by the collection of specific generalizations. In the example there may be some
values of the masses, forces, and accelerations for which there are no specific
generalizations, just because nothing ever both had that mass and was subject to that
force.
This illustrates a distinction between more fundamental laws and those derived
from them. Most basic of all are those laws that form the axioms of the optimal
system. If the laws of all the sciences can be reduced to laws of physics, as some argue
is true, at least for chemistry, then the basic laws will be the fundamental laws of
physics. If, on the other hand, there is some field the laws of which are not reducible,
then the basic laws will include laws of that field. It might be that we do not yet
actually know any basic laws -- all the laws we are acquainted with would then be
derived laws.
Laws and accidents
I hope that it should now appear that the systematic view of laws is a considerable
improvement on the SRT. While it still has problems, the account looks very much as
if it is materially adequate. An analysis of a concept is materially adequate if it is true
that were anything to be a case of the concept (the analysandum -- the thing to be
analysed) it would also be a case of the analysis, and vice versa. So “female fox” is a
materially adequate analysis of “vixen” only when it is true that if something were a
female fox it would also be a vixen, and if something were a vixen it would also be a
female fox. The systematic account looks to be materially adequate because the
13 This is the view favored by David Lewis. See his Counterfactuals, p. 73.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
13
regularities that are part of or consequences of the optimal system are precisely the
regularities we would identify as nomic regularities (regularities of natural law).
In this section I want to argue that this is an illusion, that it is perfectly possible
that systematic regularities fail to correspond to the laws there are. And in the next
section we will see that even if, as a matter of fact, laws and systematic regularities
coincide, this is not because they are the same things. The point will be that there are
certain things we use laws for, in particular for explaining, for which we cannot use
regularities, however systematic. And towards the end of this chapter I shall explain
what sort of connection there is between laws and systematic regularities, and why
therefore the systematic account looks as if it is materially adequate.
Earlier on we looked at the argument that probabilistic laws were a counter-example
to minimalism. The idea was that there could be a divergence between the law and the
corresponding regularity. Although the argument is not valid, I suggested that our intuitions should be against the minimalist. More generally, I believe that our intuitions
suggest that there could be a divergence between the laws there are and the
(systematic) regularities there are.
Returning to the simple regularity theory for a moment, one reason why this theory
could not be right is that there could be a simple regularity that is merely accidental.
The fact that there is regularity is a coincidence and nothing more. These instances are
not tied together by a law that explains them all. To some extent this can be catered
for by the systematic account. For, if the regularity is a coincidence, then we might
expect to find that the events making up this regularity each have alternative
explanations in terms of a variety of other laws (i.e. each one falls under some other
regularity). If this is the case, then the systematic account would not count this
regularity as a law. For it would add little in the way of strength, since the events that
fall under it also fall under other systematic regularities, while adding it would detract
from the simplicity of the overall system.
This raises a difficult issue for the systematic theorist, and indeed for minimalists
more generally. Might not this way of excluding coincidental regularities get it wrong
and exclude genuine laws while including accidents? It might be that there is a large
number of laws each of which has only a small number of instances. These laws may
throw up some extraordinary coincidences covering a large number of events. By the
systematic account the coincidence would be counted as a law because it contributes
significantly to the strength of the system, while at the same time the real laws are
excluded because their work in systematizing the facts is made redundant by the
accidental regularities. Figure 1.2 shows a world similar to the one discussed a few
pages back. It has the same laws, but the additional facts mean that the accidental
regularities now predominate over the genuine laws -- the optimal systematization
would include the regularity that Fs are Gs but exclude the law that Hs are Gs. If
such a world is possible, and I think our intuitions suggest it is, then the systematic
regularity theory gets it wrong about which the laws are. In this way the systematic
theory fails to be materially adequate.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
Ga
Fa
Ha
Gb
Fb
Jb
Gc
Fc
Kc
Gd
Fd
Ld
]
Accidental regularity
that all Fs are Gs
Gm
Em
Hm
Gp
Ep
Jp
Gr
Er
Kr
Gr
Er
Lr
]
Accidental regularity
that all Es are Gs
Gn
Dn
Hn
Gq
Dq
Jq
Gs
Ds
Ks
Gr
Dr
Lr
]
Accidental regularity
that all Ds are Gs
14
Law that Ls are Gs
Law that Ks are Gs
Law that Js are Gs
Law that Hs are Gs
Figure 1.2
Laws, regularities, and explanation
I have mentioned that there are various things we want laws to do, which they are not
up to doing if they are mere regularities. We have already looked at a related issue.
One thing laws are supposed to do is support counterfactuals. Some opponents of the
regularity theory think that this is sufficient to show that minimalism is mistaken, but
I think that this is a difficult line to pursue (even if ultimately correct). More
promising is to argue that laws cannot do the job of explaining their instances if they
are merely regularities. Another issue is whether we can make sense of induction if laws
are just regularities.
The key to understanding why a mere regularity cannot explain its instances is the
principle that something cannot explain itself. The notion of explanation is one we will
explore in detail in the next chapter. However, for the time being, I hope it can be
agreed that for any fact F, F does not explain F -- the fact that it rained may explain
the fact that the grass is damp, but it does not explain why it rained.
As a law explains its instances, it explains all of them and, therefore, it explains the
fact that is the uniformity consisting of all of them. But a regularity cannot do this
because, according to the above-stated principle, it cannot explain itself. To spell this
out in more detail, let us imagine that there is a law that Fs are Gs. Let there in fact
be only four Fs in the world, a, b, c, and d. So the generalization “all Fs are Gs” is
equivalent to
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
15
(A) (Fa & Ga) & (Fb & Gb) & (Fc & Gc) & (Fd & Gd) & (nothing is F other than a,
b, c, or d).
The conjunction of all the instances is
(B)
(Fa & Ga) & (Fb & Gb) & (Fc Gc) & (Fd & Gd)
(A) and (B) are identical except for the last part of (A), which says that nothing is F
other than a, b, c, or d. Let us call this bit (C)
(C)
nothing is F other than a, b, c, or d
So (A) = (B) & (C).
Thus, to say (A) explains (B) is the same as saying (B) & (C) explains (B). But
how can that be? For clearly (B) does not explain (B), as already discussed. So if (B)
& (C) explains (B) it is by virtue of the fact that (C). However, (C) says that nothing
is F other than a, b, c, or d. That other things are not F cannot contribute to explaining why these things are G. Therefore, nothing referred to in (A) can explain why it is
the case that (B).
That we have considered a law with just four instances is immaterial. The
argument can be extended to any finite number of instances. Many laws do have only
a finite number of actual instances (biological laws for example). Nor does moving to
an infinite number of instances change the nature of the argument. Even if it were
thought that the infinite case might be different, then we could give essentially the
same argument but, instead of considering the conjunction of instances, we could focus
on just one instance. Why is a, which is an F, also a G? Could being told that all Fs
are G explain this? To say that all Fs are Gs is to say if a is an F then a is a G, and all
other Fs are Gs. The question of why a, which is an F is also a G is not explained by
saying that if a is an F then a is a G, because that is what we want explained. On the
other hand, facts about other Fs even all of them, simply do not impinge on this F.
It should be noted that this objection covers, in effect, all the forms of the regularity
theory, not just the simple regularity theory. For more sophisticated versions operate
by paring down the range of regularities eligible as laws and exclude those that fail
some sort of test. But they still maintain that the essence of lawhood is to be a
regularity, and the relation of explanation between law and instance is still, according
to the regularity theorist, the relation between a regularity and the instance of the
regularity. However sophisticated a regularity theory is, it cannot then escape this
criticism. For instance, the deductive integratibility required by Lewis and Ramsey
does not serve to provide any more unity to a law than is provided by a generalization.
That the generalization is an axiom or consequence of the optimal axiomatic system
does nothing to change the fact that it or the regularity it describes cannot explain its
instances.
A case that seems to go against this may in fact be seen to prove to rule. I have an
electric toaster that seems to have a fault. I take it back to the shop where I bought it,
where I am told “They all do that, sir”. This seems to explain my problem. Whether
or not I am happy, at least I have had it explained why my toaster behaves the way it
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
16
does. However, I think that this is an illusion. Being told that Emily’s toaster does
this, and Ned’s and Ian’s too does not really explain why my toaster does this. After
all, if Emily wants to know why her toaster behaves that way, she is going to be told
that Ned’s does that too and Ian’s and so does mine. So part of the explanation of
why mine does this is that Emily’s does and part of the explanation of why Emily’s
does this is that mine does. This looks slightly circular, and when we consider everyone
asking why their toaster does this strange thing, we can see that the explanations we
are all being given are completely circular.
So why does being told “They all do that” look like an explanation? The answer is
that, although it is not itself an explanation, it points to an explanation. “They all do
that” rules out as unlikely the possibilities that it is the way I have mistreated the
toaster, or that it is a one-off fault. In the context of all the other toasters behaving
this way, the best explanation of why my toaster does so is that some feature or
by-product of the design or manufacturing process causes the toaster to do this. This
is a genuine explanation, and it is because this is clearly suggested by the shopkeeper’s
remark that the remark appears to be explanatory. What this serves to show is
precisely that regularities are not explanations of their instances. What explains the
instances is something that explains the regularity, although the fact of the regularity
may provide evidence that suggests what that explanation is.
Laws, regularities, and induction
If regularities do not explain their instances, then a question is raised about inductive
arguments from observed instances to generalizations. The critic of minimalism, whom
I shall call the fullblooded theorist says that laws explain their instances and that
inferring a law from the observation of its instances is a case of inference to the best
explanation -- e.g. we infer that there is a law of gravitation, because such a law is the
best explanation of the observed behaviour of bodies (such as the orbits of the planets
and the acceleration of falling objects). (Inference to the best explanation is discussed
in Chapters 2 and 4). Because, as we have seen, the minimalist is unable to make sense
of the idea of a law explaining its instances, the minimalist is also unable to employ this
inference-to-the-best-explanation view of inductive inference.14 For the minimalist,
induction will in essence be a matter of finding observed regularities and extending
them into the unobserved. So, while the minimalist’s induction is of the form all
observed Fs are Gs therefore all Fs are Gs, the full-blooded theorist’s induction has an
intermediate step: all observed Fs are Gs, the best explanation of which is that there is
a law that Fs are Gs, and therefore all Fs are Gs.
Now recall the problem of spurious (accidental, contrived, single case, and trivial)
regularities that faced the simple regularity theory. The systematic regularity theory
solves this problem by showing that these do not play a part in our optimal
gystematization. Note that this solution does not depend on saying that these
regularities are in themselves different from genuine laws -- e.g. it does not say that the
relationship between an accidental regularity and its instances is any different from the
14 This view is promoted by David Armstrong in his What is a law of nature?, pp. 52-9.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
17
relationship between a law and its instances. What, according to the minimalist, distinguishes a spurious regularity from a law is only its relations with other regularities.
What this means is that a minimalist’s law possesses no more intrinsic unity than does
a spurious regularity.
Recall the definition of “grue” (see p. 18). Now define “emerire” thus:
X is an emerire = either X is an emerald and observed before midnight on 31
December 2000
or X is a sapphire and not observed before midnight on 31
December 2000.
On the assumption that, due to the laws of nature, all emeralds are green and all
sapphires are blue, it follows that all emerires are grue. The idea here is not of a false
generalization (such as emeralds are grue), but of a mongrel true generalization formed
by splicing two halves of distinct true generalizations together. Now consider someone
who has observed many emeralds up until midday on 31 December 2000. If their past
experience makes them think that all emeralds are green, then they will induce that an
emerald first observed tomorrow will be green; but if they hit upon the contrived (but
real) regularity that all emerires are grue, then they will believe that a sapphire first
observed tomorrow will be blue. As both generalizations are true, neither will lead this
person astray. The issue here is not like Hume’s or Goodman’s problems -- how we
know which of many possible generalizations is true. Instead we have two true
generalizations, one of which we think is appropriate for induction and another which is
not -- even though it is true that the sapphire is blue, we cannot know this just by
looking at emeralds. What makes the difference? Whatever it is, it will have to be
something that forges a link between past emeralds and tomorrow’s emerald, a link
that is lacking between the past emeralds and tomorrow’s sapphire.
I argued, a couple of paragraphs back, that in the minimalist’s view there is no
intrinsic difference between a spurious regularity and a law in terms of their relations
with their instances. And so the minimalist is unable to give a satisfactory answer to
the question: What makes the difference between inducing with the emerald law and
inducing with the emerire regularity? Being intrinsically only a regularity the law does
not supply the required link between past emeralds and future emeralds; any link it
does provide is just the same as the one provided by the emerire regularity that links
emeralds and sapphires. (Incidentally, the case may be even worse for the systematic
regularity theorist, as it does seem as if the emerire regularity should turn out to be a
derived law because it is derivable from two other laws.)
The full-blooded view appears to have the advantage here. For, if laws are distinct
from the regularities that they explain, then we can say what makes the difference
between the emerald law and the emerire regularity. In the former case we have something that explains why we have seen only green emeralds and so is relevant to the next
emerald, while the emerire regularity has no explanatory power. It is the explanatory
role of laws that provides, unity to its instances -- they are,all explained by the same
thing. The contrast between the minimalist and full-blooded views might be illustrated
by this analogy: siblings may look very similar (the regularity), but the tie that bindi
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
18
them is not this, but rather their being born of the same parents, which explains the
regularity of their similar appearance.
3. A full-blooded view- nomic necessitation
The conclusion reached is this. A regularity cannot explain its instances in the way a
law of nature ought to. This rules out regularity theories of lawhood. The same view is
achieved from the reverse perspective. We cannot infer a regularity from its instances
unless there is something stronger than the regularity itself binding the instances
together.
The task now is to spell out what has hitherto been little more than a metaphor, i.e.
there is something that binds the instances of a law together which is more than their
being instances of a regularity, and a law provides a unity not provided by a regularity.
The suggestion briefly canvassed above is that we must consider the law that Fs are Gs
not as a regularity but as some sort of relation between the properties or universals
Fness and Gness.
The term universal refers to properties and relations that, unlike particular things,
can apply to more than one object. A typical universal may belong to more than one
thing, at different places but at the same time, thus greenness is a property that many
different things may have, possessing it simultaneously in many places. A first-order
universal is a property of or relation among particular things; so greenness is a
first-order universal. Other first-order universals would be, for example: being (made of
magnesium, being a member of the species Homo sapiens, being combustible in air, and
having a mass of 10 kg. A second-order universal is a property of or relation among
first-order universals. The property of being a property of emeralds is a second-order
universal since it is a property of a property of things. The first order universal
greenness has thus the second-order property being a colour. Being generous is a
first-order property that people can have. Being a desirable trait is a property that
properties can have - for instance, being generous has the property of being desirable;
so the latter is a second-order universal.
Consider the law that magnesium is combustible in air. According to the
full-blooded view this law is a relation between the properties of being magnesium and
being combustible in air. This is a relation of natural necessity. It is not just that
whenever the one property is instantiated the other is instantiated, which would be the
regularity view. Rather, necessitation is supposed to be stronger. The presence of the
one property brings about the presence of the other. Necessitation is therefore a
property (more accurately a relation) of properties. This is illustrated in Figure 1.3,
where the three levels of particular things, properties of those things (first order
universals) and relations among properties (second order universals) are shown. The
arrow, which represents the law that emeralds are green, is to be interpreted as the
relation of necessitation holding between the property of being an emerald and the
property of being green.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
19
Laws involve
Necessitation
which is a (second-order) relation among
Being
magnesium
→
Being combustible
in air
which are (first-order) properties of
Particular things
Figure 1.3
The advantages of this view are that it bypasses many of the problems facing the
minimalist. Many of those problems involved accidental regularities or spurious
“cooked-up” regularities. What were problems for the minimalist now simply disappear
- necessitation among universals is quite a different matter from a regularity among
things. The existence of a regularity is a much weaker fact than necessitation between
universals. Two universals can coexist in precisely the same objects without one
necessitating the other. We would have something like the diagram in Figure 1.3, but
without the top layer and so without the arrow. This is the case in a purely accidental
regularity. In an accidental regularity every particular has both of two universals, but
the universals are not themselves related. This explains why not every regularity is a
law. It also explains why every deterministic law entails a regularity. If there is a law
that Fness necessitates Gness then every F will be G. This is because if x is F then the
presence of Fness in x will bring about Gness in x, i.e. x will be G. So the existence of a
deterministic law will bring about the corresponding regularity without the reverse
holding.
This deals with accidental regularities. Some of the more spurious regularities, for
instance those employing grue-type predicates, are even more easily dealt with, because
the cooked-up predicates do not correspond to universals. There need be no genuine
property of being grue, and hence none to be related by nomic necessitation.
Nomic necessitation among universals also makes more sense of explanation and
induction. Regularities, we saw, cannot explain their instances in the way that laws are
supposed to, as to do so would be circular. No such problem arises for the full-blooded
view. The fact of a’s being both F and G and the general fact of all Fs being Gs are
both quite distinct from the fact of Fness necessitating Gness. The former are facts
about individuals, while the latter is a fact about universals. And, as explained, while
the latter fact entails the regularity that all Fs are Gs, it also goes beyond it, as it is
not entailed by it. So reference to necessitation among universals as an explanation of
particular facts or regularities is genuinely informative.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
20
It also provides the unity among instances of a law that is necessary for induction
to be possible. The thought is that if we see various different pieces of magnesium
burn in air, we can surmise that the one property, being magnesium, necessitates the
other, combustibility. If this conclusion is correct, then this relation will show itself in
other pieces of magnesium. We induce not merely a resemblance of unobserved cases to
those we have seen, but rather we induce a single fact, the relation of these two
properties, which brings about the resemblance of unobserved to observed cases. In
this way we should think of induction to facts about the future or other unobserved
facts not as a one-stage process:
All observed Fs are Gs
∴all unobserved Fs are Gs
but instead as a two-stage process
All observed Fs are Gs
∴Fness necessitates Gness
∴all unobserved Fs are Gs
What is necessitation?
So far so good. The idea of necessitation between universals seems to do the job
required of it better than the minimalist’s regularities, be they systematic or otherwise.
The objection the minimalist has the right to raise is this. At least we know what we
mean by regularity. But what do we mean by necessitation? It is not something we
can see. Even if in a God-like manner we could see all occurrences of everything
throughout time and space, we would still not see any necessitation. The necessitation
of Gness by Fness looks just like the regularity of Fs being Gs. This may not be
enough to show that there is nothing more to a law than being a regularity. But it
does put the onus on the full-blooded theorist. For without a satisfactory answer the
suspicion may remain that perhaps “Fness necessitates Gness” just means “there is a
law that Fs are Gs”, in which case the full-blooded theorist will really be saying nothing
at all.
What then can we say about this notion of “necessitation”? A leading full-blooded
theorist, David Armstrong, lists the following properties of necessitation, which you will
recognize from our discussion:
(1) If Fness necessitates Gness then this entails that everything which is F is also G.
(2) The reverse entailment does not follow. Instances of Fness may only coincidentally
also be instances of Gness, without the being any necessitation.
(3) Since necessitation is a relation, it is a universal. Furthermore, since necessitation
is a relation among universals, it is a second-order universal.
(4) Since necessitation is a universal it has instances. Its instances are cases of, for
example, a’s being G because a is F (a’s being F necessitates a’s being G).
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
21
Is this enough to tell us what necessitation is? It might be thought that if we listed
enough of the properties of necessitation, then that would be sufficient to isolate the
relation we are talking about. If I told you that I was thinking about a relation R, and
that R is a relation among people that is used to explain why people have the genetic
properties they do, then you would be able to work out that what I had in mind was
something like the relation “being an ancestor of”. So perhaps the properties (l)-(4) are
sufficient to isolate the relation of necessitation.
In fact, it turns out that these conditions do not succeed in distinguishing the
nomic necessitation view from the regularity view of laws.15 To see this let the relation
RL be taken to hold between universals F and G precisely when it is a law that Fs are
Gs, according to the Ramsey-Lewis systematic account. The requirements on RL are as
follows:
The properties F and G are RL related precisely when:
(a) all Fs are Gs;
(b) the above is an axiom or theorem of that axiomatic system which captures the
complete history of the universe and is the maximal combination of strength and
simplicity.
The point is that the RL relation does everything that necessitation is supposed to
do according to Armstrong’s properties (1)-(4). Let us take (l)-(4) in turn: (1) If F
and G are RL related, then, by (a), all Fs are also Gs. (2) Because of (b) the reverse
entailment does not follow. (3) The RL relation is a relation among properties. Hence
it is a second-order relation. (4) We can regard “a’s being G because a is F” as an
instance of the RL relation -- when F and G are RL related, a is both F and G, and the
capturing of the fact that a is G by the regularity that all Fs are Gs contributes to the
systematization mentioned in (b). (I discuss this point at greater length in the next
chapter.)
As the requirements (1)-(4) can be satisfied by taking laws to be a certain species of
regularity, these requirements cannot gives us any insight into necessitation that
accounts for the most important metaphysical features of laws, i.e. those which we
discussed above:
(i) a law explains its instances;
(ii) particular facts can count as evidence for there being a law;
(iii) it is possible for systematic regularities to diverge from the laws that there are (i.e.
there can be a lot of systematic regularity for which there are no corresponding
laws).
We could add (i)-(iii) to (1)-(4), which would then exclude RL relations. But to do
so would be to give up on trying to give an illuminating explication of the concept of
necessitation. There would be no reason for someone who is doubtful about the idea of
15 Points to this effect are made by Jeremy Butterfield in his review of Armstrong What is a law of Nature? in
Mind 94, 1985.
Excerpt from Bird, A. (1998) Philosophy of Science, McGill Queens: Montreal, pp. 25-54.
22
necessitation to think that such a relation really exists. Thus an alternative account of
necessitation that satisfies (1)-(4) and (i)-(iii) is still required. This is what I will try to
provide next.